Karl Glasner
Abstract:
We analyze rigorously the one-dimensional traveling wave problem for a
thermodynamically consistent phase field model. Existence is proved
for two new cases: one where the undercooling is large but not in the
hypercooled regime, and the other for waves which leave behind an unstable
state. The qualitative structure of the wave is studied, and under
certain restrictions monotonicity of front profiles can be obtained.
Further results, such as a bound on propagation velocity and non-existence
are discussed. Finally, some numerical examples of monotone and
non-monotone waves are provided.
Submitted January 4, 2000. Published February 25, 2000.
Math Subject Classifications: 80A22, 74J30.
Key Words: Traveling waves, Phase field models.
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